You're right, the angular velocity should have a direction. If I recall correctly, you can use the right-hand-rule: if you curl your fingers in the direction that it's rotating and stick your thumb out, the direction of your thumb is the direction of the angular velocity. So, for example, if you're looking at a clock head on, your right hand fingers will curl clock-wise (they better if you're looking at a clock!) and your thumb will point towards the clock, through the wall, so the direction of angular velocity of the hands is through the wall.

In English you have two terms for the same thing, speed as a quantity and velocity as a vector (curiously in spanish, a language with a huge vocabulary, we use "velocidad" for that two things) and you can distinguish. Most of books which were not english original, may be bad translated. Its very frecuently...

The major part of physics books that I have are Spanish-translated, so there ary many concepts that are not very good translated, such as "speed" or "velocity" that we can't distinguish :)

Yep, I think AKG has it. The formula your book has is probably one for the magnitude of the angular velocity, which is the same as the angular speed. The direction of the angular velocity is as AKG said, using the right-hand convention, likewise the direction of the angular momentum.

I have a book that gives a formulae Angular Speed as same as the Angular Velocity.....is that true?

From what i understand, speed is a scalar quantity.....so it only have the magnitude value while velocity is a vector quantity which also shows the direction.

Also, will the average angular speed = average angular velocity? The same book states its the same....but I have doubt on that statement .....could anyone help me in this? Thanks in advance

Technically, they're not the same. But, if you're analyzing 2-dimensional objects (circles, ellipses, etc), you're probably better off treating them as the same.

For 2-dimensional objects lying in the fundamental plane, the angular velocity vector only has one component - and it is perpendicular to the plane of the circle/ellipse (either up or down, depending on whether the rotation is counterclockwise or clockwise).

For example, if you're trying to find linear velocity on a circle of radius r and an angular velocity w (closest I can come to little omega in text), the 'proper' way is to take the cross product of vectors w and r, or multiply the scalar value of w by the scalar value of r times the sine of the angle between the two vectors, or, knowing the sine of 90 degrees is 1, you could just use the scalar equation: radius length times angular speed (usually the most sensible way).

In English you have two terms for the same thing, speed as a quantity and velocity as a vector (curiously in spanish, a language with a huge vocabulary, we use "velocidad" for that two things) and you can distinguish. Most of books which were not english original, may be bad translated. Its very frecuently...

These is even more so in the computer science field here in Latin America. I remember reading through two database books (one translated in Mexico and the other in Spain). The word for tuple in the 'mexican' book was "tuple" while in the 'spanish' book it was "tupla". Another example is the word key which the 'mexican' book translated as "llave" and the 'spanish' book as "clave". Talk about confusing.

Speed in spanish translates to 'rapidez' while velocity is 'velocidad'. Why people decide to use only 'velocidad' is beyond me. This reminds me when I was learning german and I asked my dad (who is german) what speed is in german and he said 'Geschwindigkeit'. I later found out that he was incorrect because the proper word is 'Tempo'. I guess for the sake of simplicity people use one term to refer to both things.